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Top cross-section @ NNLO

Top cross-section @ NNLO. Alexander Mitov Theory Division, CERN. Will discuss total inclusive x -section Useful for normalizations Aim at precision D ifferential in future work (2013+). The story of top pair production. Early NLO QCD results (inclusive, semi-inclusive)

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Top cross-section @ NNLO

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  1. Top cross-section @ NNLO Alexander Mitov Theory Division, CERN Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  2. Will discuss total inclusive x-section • Useful for normalizations • Aim at precision • Differential in future work (2013+) Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  3. The story of top pair production • Early NLO QCD results (inclusive, semi-inclusive) • First fully differential NLO • 1990’s: the rise of the soft gluon resummation at NLL • NNLL resummation developed (and approximate NNLO approaches) • Electroweak effects at NLO known (small ~ 1.5%) • NNLO QCD corrections Nason, Dawson, Ellis ‘88 Beenakkeret al ‘89 Mangano, Nason, Ridolfi’ 92 Catani, Mangano, Nason, Trentadue ’96 Kidonakis, Sterman ’97 Bonciani, Catani, Mangano, Nason `98 Beneke, Falgari, Schwinn ‘09 Czakon, Mitov, Sterman `09 Beneke, Czakon, Falgari, Mitov, Schwinn `09 Ahrens, Ferroglia, Neubert, Pecjak, Yang `10-`11 Beenakker, Denner, Hollik, Mertig, Sack, Wackeroth `93 Hollik, Kollar `07 Kuhn, Scharf, Uwer ‘07 Bärnreuther, Czakon, Mitov `12 Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  4. Until 6 moths ago σTOT analyzed exclusively in approximate NNLO QCD Beneke, Falgari, Klein,Schwinn `09-`11 Ahrens, Ferroglia, Neubert, Pecjak, Yang `10-`11 Kidonakis `03-`11 Aliev, Lacker, Langenfeld, Moch, Uwer, Wiedermann ’10 Cacciari, Czakon, Mangano, Mitov, Nason ‘11 • To study approx NNLO is theoretically very interesting but is it pheno game changer? • No. • This should not come as surprise. This was first noticed in 1998 at NLO+NLL Bonciani, Catani, Mangano, Nason ‘98 Conclusion: resummed result alone does not approximate the exact NLO very well. additional power suppressed terms are needed. Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  5. Indeed, comparison between various NNLOapprox groups shows: Beneke, Falgari, Klein, Schwinn `11 • Significant differences between various predictions • Suggests the true uncertainty of approximate NNLO • (originates beyond the approximation) Cacciari, Czakon, Mangano, Mitov, Nason ‘11 Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  6. Here is the proof we understand the physics well Plots: M. Beneke, CKM 2012 Topixs Top++ Topixs Top++ After NNLO Before NNLO • It was established that approx NNLO is dominated by unknown NNLO effects, not resummation • The inclusion of the full NNLO proves that (see above): perfect agreement now between • different resummations Cacciari, Czakon, Mangano, Mitov, Nason ‘11 • Mellin space resummation with Top++(1.3) • Current version 1.4 (includes all available NNLO results + resummation) Czakon, Mitov arXiv:1112.5675 • x-space resummation with Topixs Beneke, Falgari, Klein, Piclum, Schwinn, Ubiali, Yan ‘12 Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  7. Towards complete NNLO result • First ever hadron collider calculation at NNLO with more than 2 colored partons. • First ever NNLO hadron collider calculation with massive fermions. • Published qQtt +X • Published all fermionic reactions (qq,qq’,qQ’) • Published gq • Work on the only remaining reaction gg progressing well: • Barring unexpected computing slowdown, • sound estimate for gg (if not the full result) should be available within 1 month. Bärnreuther, Czakon, Mitov `12 Czakon, Mitov `12 Czakon, Mitov `12 Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  8. Independent F/R scales • MSTW2008NNLO • mt=173.3 NNLO phenomenology at the Tevatron: P. Bärnreuther et al arXiv:1204.5201 NNLO Best prediction at NNLO+NNLL • Two loop hard matching coefficient extracted and included • Very week dependence on unknown parameters (sub 1%): gg NNLO, A, etc. • ~ 50% scales reduction compared to the NLO+NNLL analysis of Cacciari, Czakon, Mangano, Mitov, Nason ‘11 Resumed (approximate NNLO) Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  9. Independent F/R scales • mt=173.3 Good perturbative convergence: P. Bärnreuther et al arXiv:1204.5201 • Good overlap of various orders (LO, NLO, NNLO). • Suggests our (restricted) independent scale variation is good Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  10. Independent F/R scales • MSTW2008NNLO • mt=173.3 NNLO phenomenology at the LHC: Czakon, Mitov arXiv:1210.6832 Best prediction at (N)NLO+NNLL • 5% scale uncertainty • Good agreement with LHC measurements • Clearly, main uncertainty from unknown NNLO gg terms Decrease of scale variation due to currently known NNLO corrections @ LHC: by ±1% (from qQ) by ±2% (from gq) Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  11. An often asked question (recall CMSαSmeasurement): • which one of the many theory predictions should we use? • It was suggested to use the high-energy limit • of the X-section to predict it everywhere: • MUV approximation dramatically deviates • from the exact gq NNLO result • Leads to large difference for the x-section • O(5%) from gq alone ! • Similar deviation for qq->tT+X (flux included) Moch, Uwer, Vogt ’12 (included in Hathor 1.3 by Aliev et al ‘10) Czakon, Mitov arXiv:1210.6832 Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  12. Summary and Conclusions • Moving from approximate NNLO to complete NNLO • Resummation does improve theory, but alone is not a game changer: • Approximate NNLO (in name) • Almost NLO+NLL (in predictive power) • Besides gg, all partonic reactions known to NNLO. • At Tevatron this is sufficient for full NNLO phenomenology • At LHC 5% non-pdf theory uncertainty. • gg will be available very soon O(weeks) + time needed to make it public. • Any suggestions about how to make the results more useful will be highly appreciated Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  13. Backup slides Top cross-section @ NNLO Alexander Mitov Top LHC Working Group, CERN, 29 Nov 2012

  14. Structure of the cross-section Relative velocity of tT • The partonic cross-section computed numerically in 80 points. Then fitted. • Many contributing partonic channels: Computed. Dominant at Tevatron (~85%) All of the same complexity. No more conceptual challenges expected (just lots of CPU) Precision top pair production Alexander Mitov Göttingen, 02 Nov, 2012

  15. Results @ parton level: qqbar -> ttbar +X • Notable features: • Small numerical errors • Agrees with limits Partonic cross-section through NNLO: The NNLO term: Analytic Numeric The known threshold approximation P. Bärnreutheret al arXiv:1204.5201 Beneke, Czakon, Falgari, Mitov, Schwinn `09 Precision top pair production Alexander Mitov Göttingen, 02 Nov, 2012

  16. P. Bärnreutheret al arXiv:1204.5201 Results @ parton level: qqbar -> ttbar +X An alternative view of the partonic cross-sections: Bärnreuther, Czakon, Mitov `12 Precision top pair production Alexander Mitov Göttingen, 02 Nov, 2012

  17. Results @ parton level: The all-fermionic reactions Czakon, Mitov ‘12 P. Bärnreutheret al arXiv:1204.5201 These partonic cross-sections are very small. Compare to the ones involving gluons! • Had to compute up to beta=0.9999 to get the high-energy behavior right. Precision top pair production Alexander Mitov Göttingen, 02 Nov, 2012

  18. Results @ parton level: The all-fermionic reactions The interesting feature: high-energy logarithmic rise: Predicted in analytical form Ball, Ellis `01 • Direct extraction from the fits. • 5% uncertainty. Czakon, Mitov ‘12 • Agrees with independent prediction. • 50% uncertainty. Moch, Uwer, Vogt ‘12 High-energy expansion non-convergent. Applies only to the high-energy limit. Czakon, Mitov ‘12 Precision top pair production Alexander Mitov Göttingen, 02 Nov, 2012

  19. Results @ parton level:qg -> ttbar +X Czakon, Mitov `12 • Correction about -1% (Tev and LHC). • Notable decrease of scale dependence at LHC. • NNLO large compared to NLO. • High-energy log-limit correct • Agree for the constant with • The limit itself plays noPheno role Ball, Ellis `01 Moch, Uwer, Vogt ‘12 Precision top pair production Alexander Mitov Göttingen, 02 Nov, 2012

  20. Results @ parton level:qg -> ttbar +X Czakon, Mitov `12 X-section times flux Tevatron LHC 8 TeV Precision top pair production Alexander Mitov Göttingen, 02 Nov, 2012

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